Correlations for pairs of closed geodesics
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- Pollicott, M. & Sharp, R. Invent. math. (2006) 163: 1. doi:10.1007/s00222-004-0427-7
In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems have been studied in both Quantum Chaos and number theory.